Q. 43.9( 35 Votes )

# Show that the points (2, 3, 4), (–1, –2, 1), (5, 8, 7) are collinear.

Answer :

If the direction ratios of two lines segments are proportional, then the lines are collinear.

Given A(2, 3, 4), B(−1, −2, 1), C(5, 8, 7)

Direction ratio of line joining A (2,3,4) and B (−1, −2, 1), are

(−1−2), (−2−3), (1−4)

= (−3, −5, −3)

So a_{1} = -3, b_{1} = -5, c_{1} = -3

Direction ratio of line joining B (−1, −2, 1) and C (5, 8, 7) are

(5− (−1)), (8−(−2)), (7−1)

= (6, 10, 6)

So a_{2} = 6, b_{2} = 10 and c_{2} =6

It is clear that the direction ratios of AB and BC are of same proportions

As

and

Therefore A, B, C are collinear.

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